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2019 | z. 171 | 19--36
Tytuł artykułu

Optymalna strategia inwestycyjna na rynku finansowym Blacka-Scholesa-Mertona typu Lévy'ego

Autorzy
Warianty tytułu
Lévy-Type Black-Scholes-Merton Optimal Investment Strategy in the Financial Market
Języki publikacji
PL
Abstrakty
Celem badań jest znalezienie optymalnej strategii inwestycyjnej na zupełnym rynku finansowym Blacka-Scholesa-Mertona typu Lévy'ego bez arbitrażu. W artykule wyznaczono udziały różnych instrumentów finansowych w portfelu optymalnym. Ceny tych instrumentów opisane są za pomocą procesu Levy'ego, który jest uogólnieniem procesu Wienera. Ponadto założono, że współczynniki modelu zależą od stanów łańcucha Markowa. Taki rynek jest niezupełny, co oznacza, że nie każdą wypłatę można zreplikować za pomocą pewnej strategii inwestycyjnej. Aby uzupełnić ten rynek, dodano skokowe instrumenty finansowe oraz aktywa potęgowo skokowe. Następnie wykorzystano metody programowania dynamicznego do wyznaczenia optymalnej strategii inwestycyjnej na tym rynku. Optymalna strategia to taka, która maksymalizuje oczekiwaną użyteczność procesu bogacenia na końcu ustalonego z góry okresu. Analizę przeprowadzono dla logarytmicznej i potęgowej funkcji użyteczności wypłaty. (abstrakt oryginalny)
EN
The study was motivated by searches for an optimal Lévy-type investment strategy in a Black-ScholesMerton complete financial market with no arbitrage. The paper stipulates shares of various financial instruments in an optimal portfolio. Their prices are described using Lévy processes, which are a generalised Wiener process. On top of that, an assumption was made about model indicators, which depend on Markov chains. This is an incomplete market meaning not every payment can be replicated using a certain investment strategy. In order to complete the market, jump financial instruments and power-jump assets have been added. Next, dynamic programming methods were deployed to determine an optimal investment strategy in this market. An optimal strategy is the one which maximises the expected utility of wealth accumulation at the end of a pre-determined period. The analysis was carried out for a logarithmic and power function of utility of the received payment. (original abstract)
Twórcy
autor
  • Uniwersytet Ekonomiczny we Wrocławiu
Bibliografia
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171552375

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